MGMT 675
AI-Assisted Financial Analysis
Trees and Forests
Outline
- Decision tree
- Random forest and gradient boosting
- Shapley values
- House price application
- Missing values
- Dummy variables
- Scaling
Decision tree
- Split dataset into subsets. Within each subset, \(\hat y=\) mean of subset. Calculate MSE.
- Split each subset into further subsets and continue.
- Use means of subsets to estimate. Choose splits to minimize MSE.
Example
- Ask Julius to read irrelevant_features.xlsx.
- Ask Julius to fit a decision tree regressor with y1 as the target using all of the data as training data. Ask Julius to plot the tree.
Random forest and gradient boosting
Random Forest
- Generate random datasets of the same size as the original.
- Create the random datasets by randomly drawing rows from the original with replacement.
- Fit a decision tree to each random dataset.
- The prediction for any observation is the average of the predictions of the various trees.
- Randomization helps to avoid overfitting.
- Also control overfitting through:
- max_depth = maximum number of times to split in each tree
- max_features = number of features to look at when deciding how to split (a subset of features of that size is randomly chosen for each split)
Gradient Boosting
- Fit a decision tree.
- Look at its errors. Fit a new decision tree to predict the errors.
- New prediction is original plus a fraction of the prediction of original’s error (fraction = learning rate).
- Look at the errors of the new predictions. Fit a new decision to predict these errors.
- Continue …
Examples
Ask Julius to train and test
- a random forest regressor
- a gradient boosting regressor
to predict y1 in irrelevant_features.xlsx.
Ask Julius to use GridSearchCV to
find the best max_depth for the random forest regressor in (5, 10, 15, 20, 25)
find the best learning rate for the gradient boosting regressor in (0.001, 0.005, 0.01, 0.05, 0.1, 0.2)
Interpreting Models: Shapley Values
- The Shapley value for a feature at an observation is a measure of how much that feature contributed to the prediction at that observation.
- A summary of Shapley values is a bar chart showing the mean absolute contribution of each feature (mean across observations).
- A Shapley scatter plot for a feature plots all of the observations with the feature’s value on the x axis and the feature’s contribution to the prediction on the y axis.
- Ask Julius to create a summary plot of the Shapley values for the random forest regressor with the best max_depth.
- Ask Julius to create a scatter plot of the Shapley values for the x1 feature.
- Ask Julius to create a scatter plot of the Shapley values for another feature.
Valuing Houses
Data
- Download house_price.xlsx from the course website
- Upload the file to Julius.
- Ask Julius to read the data and describe it.
- Tell Julius that SalePrice is the target and the other columns are features.
New topics
- Missing values. Possible solutions:
- Fill in missing values
- Drop columns with missing values
- Drop rows with missing values
- Categorical variables. Convert to dummies.
- Scaling features. It is important for some models that features be on the same scale.
Missing Values
Tell Julius to fill in missing values
for categorical features with “None”
for numeric features with 0.
Dummy variables
Categorical
| Feature | |
|---|---|
| Row1 | Hi |
| Row2 | Lo |
| Row3 | Med |
| Row4 | Med |
| Row5 | Lo |
Dummies
| Lo | Med | Hi | |
|---|---|---|---|
| Row1 | 0 | 0 | 1 |
| Row2 | 1 | 0 | 0 |
| Row3 | 0 | 1 | 0 |
| Row4 | 0 | 1 | 0 |
| Row5 | 1 | 0 | 0 |
Pipeline
Ask Julius to create a pipeline that
- transforms the qualitative features to dummy variables
- applies Standard Scaler to the numeric features
- applies a random forest regressor
Train and test
Ask Julius to train and test the pipeline.
Further work
- Apply GridSearchCV to the pipeline to find best hyperparameters
- Replace random forest regressor with other models:
- lasso regressor
- ridge regressor
- gradient boosting regressor